The generator matrix

 1  0  0  0  1  1  1  X  1 a^2*X  1  1  1  1  1  X  1  1  0  X  1  1  0  1  1  1  1  1  1  1  1 a^2*X  0  X  1  1  1  1  1  1  1  1  1  1  1  1
 0  1  0  0  X  1 X+1  1 a*X  1 a^2*X+a X+a^2 a^2 a*X+1 a^2*X+1  1 X+a  a  1  1 a^2*X  1  1  1 X+a^2  0 a*X a^2*X+a^2 a^2  X X+a^2  X  1  1 a*X+a a^2 a^2*X a^2*X+a^2  1 a^2*X+1 a*X+1 a^2*X+1  X a*X+a^2 X+a^2  1
 0  0  1  0 a^2*X+1  1 a^2*X a^2*X+1 X+1 a^2*X+a a^2*X+a^2  X a^2*X+a^2 X+a a^2 a^2*X+a  0 a^2*X+a a*X  1 a^2 a*X+1  a X+a X+a a*X+1 a^2*X X+1 X+1  a a*X+a  1  X a^2*X+a^2 X+a^2 a^2*X+a a*X+a a^2 a*X a*X  a  1 a^2*X+a^2 a^2*X+1  a a^2*X+a
 0  0  0  1 a^2  X a*X+a^2 a*X+a^2  a a^2*X X+a a^2*X+a^2 a^2*X+1 a*X+1 a*X+a^2 a^2*X+a X+1 a*X a*X+1 a*X+a a^2*X+a^2  1  1 a^2*X+a^2 a*X+a^2 a*X+1  1 X+1 X+a a*X+a X+a a^2*X+a^2 a^2*X+a X+a^2 a^2*X+a^2 a*X+1  1  X a^2*X+a  X  0 X+a^2 X+a X+a^2 a^2*X a^2*X+a^2

generates a code of length 46 over F4[X]/(X^2) who´s minimum homogenous weight is 124.

Homogenous weight enumerator: w(x)=1x^0+390x^124+648x^125+648x^126+864x^127+1686x^128+1812x^129+1704x^130+1776x^131+3363x^132+3180x^133+2652x^134+2604x^135+4533x^136+4152x^137+3372x^138+2892x^139+5337x^140+4884x^141+3180x^142+2772x^143+4128x^144+2856x^145+1980x^146+1236x^147+1389x^148+840x^149+288x^150+144x^151+153x^152+60x^153+9x^156+3x^160

The gray image is a linear code over GF(4) with n=184, k=8 and d=124.
This code was found by Heurico 1.16 in 11.1 seconds.